Energy Optimal Scheduling on Multiprocessors with Migration

We show that the problem of finding an energy minimal schedule for execution of a collection of jobs on a multiprocessor with job migration allowed has polynomial complexity. Each job is specified by a release time, a deadline, and an amount of work to be performed. All of the processors have the same, convex power-speed trade-off of the form P = phi(s), where P is power, s is speed, and phi is convex. Unlike previous work on multiprocessor scheduling, we place no restriction on the release times, deadlines, or amount of work to be done. We show that the scheduling problem is convex, and give an algorithm based on linear programming. We show that the optimal schedule is the same for any convex power-speed trade-off function.